The Erdős-Sós conjecture for geometric graphs - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2013

The Erdős-Sós conjecture for geometric graphs

Résumé

Let f(n,k) be the minimum number of edges that must be removed from some complete geometric graph G on n points, so that there exists a tree on k vertices that is no longer a planar subgraph of G. In this paper we show that ( 1 / 2 )n2 / k-1-n / 2≤f(n,k) ≤2 n(n-2) / k-2. For the case when k=n, we show that 2 ≤f(n,n) ≤3. For the case when k=n and G is a geometric graph on a set of points in convex position, we completely solve the problem and prove that at least three edges must be removed.
Fichier principal
Vignette du fichier
2196-7736-1-PB.pdf (269.49 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00990608 , version 1 (13-05-2014)

Identifiants

Citer

Luis Barba, Ruy Fabila-Monroy, Dolores Lara, Jesús Leaños, Cynthia Rodriguez, et al.. The Erdős-Sós conjecture for geometric graphs. Discrete Mathematics and Theoretical Computer Science, 2013, Vol. 15 no. 1 (1), pp.93--100. ⟨10.46298/dmtcs.628⟩. ⟨hal-00990608⟩

Collections

TDS-MACS
345 Consultations
1470 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More